Machinery's Handbook, 31st Edition
Shafts 301 kilograms. The factors K m , K t , and B are unchanged, and D 1 = the inside diameter of a hollow shaft in millimeters. Table 1. Recommended Values of the Combined Shock and Fatigue Factors for Various Types of Load
Stationary Shafts
Rotating Shafts
K t
K m 1.5
K t
K m 1.0
Type of Load
Gradually applied and steady Suddenly applied, minor shocks only Suddenly applied, heavy shocks
1.0
1.0
1.5–2.0
1.5–2.0
1.5–2.0 2.0–3.0
1.0–1.5 1.5–3.0
… …
Table 2. Recommended Maximum Allowable Working Stresses for Shafts Under Various Types of Load
Type of Load Simple Bending Pure Torsion
Combined Stress p t = 8000 p t = 6000
Material
S s = 8000 S s = 6000 (See note b )
S = 16,000 S = 12,000 (See note a )
“Commercial Steel” shafting without keyways “Commercial Steel” shafting with keyways Steel purchased under definite physical specs.
(See note b ) a S = 60 percent of the elastic limit in tension but not more than 36 percent of the ultimate tensile strength. b S s and p t = 30 percent of the elastic limit in tension but not more than 18 percent of the ultimate tensile strength. If the values in the Table are converted to metric SI units, note that 1000 pounds per square inch = 6.895 newtons per square millimeter. Table 3. Values of the Factor B Corresponding to Various Values of K for Hollow Shafts K D D 1 = 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 B K 1 1 4 3 ' = − ^ h 1.75 1.43 1.28 1.19 1.14 1.10 1.07 1.05 1.03 1.02 For solid shafts, B = 1 because K = 0, as follows: B K 1 1 1 1 0 1 4 3 3 ' ' = − = − = ^ ^ h h Effect of Keyways on Shaft Strength.— Keyways cut into a shaft reduce its load carrying ability, particularly when impact loads or stress reversals are involved. To ensure an ad- equate factor of safety in the design of a shaft with standard keyway (width, one-quarter, and depth, one-eighth of shaft diameter), the former Code for Transmission Shafting tentatively recommended that shafts with keyways be designed on the basis of a solid circular shaft using not more than 75 percent of the working stress recommended for the solid shaft. See also page 2539 . Formula for Shafts of Brittle Materials.— The preceding formulas are applicable to duc- tile materials and are based on the maximum-shear theory of failure which assumes that the elastic limit of a ductile material in shear is one-half its elastic limit in tension. Brittle materials are generally stronger in shear than in tension; therefore, the maximum- shear theory is not applicable. The maximum-normal-stress theory of failure is now generally accepted for the design of shafts made from brittle materials. A material may be considered brittle if its elongation in a 2-inch gage length is less than 5 percent. Materials such as cast iron, hardened tool steel, hard bronze, etc. conform to this rule. The diameter of a shaft made of a brittle material may be determined from the following formula which is based on the maximum-normal-stress theory of failure: D B 3 = + . S K M K M K T 51 t m m t 2 2 + ^ ^ ^ h h h 7 A
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